Let the vectors a, b, c be such that | a |=2,| b |=4 and | c |=4. If the projection of b on a is equal to the projection of c on a and b is…

Let the vectors $\displaystyle \overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{c}}$ be such that $\displaystyle |\overrightarrow{\mathrm{a}}|=2,|\overrightarrow{\mathrm{~b}}|=4$ and $\displaystyle |\overrightarrow{\mathrm{c}}|=4$. If the projection of $\displaystyle \vec{b}$ on $\displaystyle \vec{a}$ is equal to the projection of $\displaystyle \vec{c}$ on $\displaystyle \vec{a}$ and $\displaystyle \vec{b}$ is perpendicular to $\displaystyle \vec{c}$, then the value of $\displaystyle |\vec{a}+\vec{b}-\vec{c}|$ is \_\_\_\_.